HP 10bII+ Financial Calculator User’s Guide HP Part Number: NW239-90001 Edition 1, May 2010 i
Legal Notice This manual and any examples contained herein are provided “as is” and are subject to change without notice. Hewlett-Packard Company makes no warranty of any kind with regard to this manual, including, but not limited to, the implied warranties of merchantability, non-infringement and fitness for a particular purpose. In this regard, HP shall not be liable for technical or editorial errors or omissions contained in the manual.
HP 10bII+ Financial Calculator iii
Keyboard Map Legend iv \ SHIFT Down (orange functions on key bevel) ] Number (row of keys) Primary Functions (white) 1 12 character, sevensegment screen display 2 Time Value of Money (TVM) 3 Input key, markup, cost, Date and change of price and margin days, IRR per year, NPV, beginning/end of payment period Calendar and coupon payment schedules, settlement and maturity dates (bonds) 4 K memory register, Swap, percent change, percent, cash flow cash flow count, delete amount, statistics entry,
Table of Contents Legal Notice............................................................................................................... ii HP 10bII+ Financial Calculator.................................................................................... iii Keyboard Map Legend ............................................................................................... iv 1 At a Glance....................................................................................................................
Arithmetic with One-and Two-number Functions............................................................ 39 Last Answer ............................................................................................................. 41 Display Format of Numbers ....................................................................................... 41 Scientific Notation .................................................................................................... 43 Interchanging the Period and Comma ...
8 Cash Flow Calculations ..................................................................................................... 87 How to Use the Cash Flow Application........................................................................87 Clearing the Cash Flow Memory.................................................................................88 Calculating Internal Rate of Return...............................................................................90 NPV and IRR/YR: Discounting Cash Flows ..
Inverse of Student’s t Probability Lower Tail................................................................ 132 Conversions from Lower Tail .................................................................................... 133 13 Additional Examples .....................................................................................................137 Business Applications.............................................................................................. 137 Loans and Mortgages .............
1 At a Glance... This section is designed for you if you’re already familiar with calculator operation or financial concepts. You can use it for quick reference. The rest of the manual is filled with explanations and examples of the concepts presented in this section. Basics of Key Functions Table 1-1 Basics of key functions Keys Display = 0.00 0.00 Description Turns calculator on. Displays shift annunciator ] . [blue] 0.00 Displays shift annunciator \ [orange] JGD| M \t \N ]Oj ]OY ]OJ ]O: \> .
Shift Keys Most keys on the HP 10bII+ have three functions: • a primary function printed in white on the key. • a secondary function printed in orange on the bevel of the key. • a tertiary function printed in blue above the key on the keyboard (see Figure 1).
Table 1-2 Clearing functions Keys Associated Function ]OY ]OJ ]O: \t Clears break-even memory. Clears TVM memory. Clears cash flow memory. Clears statistics memory. For more information on the calculator’s keys and basic functions, refer to chapter 2, Getting Started. Percentages Table 1-3 Keys for percentage calculations Keys Description § \¨ À ¼ ® Ã Percent Percent change Cost Price Margin Markup Add 15% to 17.50. Table 1-4 Calculating the price Keys Jj7V:1 JV§4 Display Description 17.
Table 1-5 Finding the margin Keys JVÀ GG¼ ® Display Description 15.00 Enters cost. 22.00 Enters price. 31.82 Calculates margin. If the cost is 20.00 and the markup is 33%, what is the selling price? Table 1-6 Calculating the price Keys Display Description G:À DDÃ ¼ 20.00 Enters cost. 33.00 Enters markup. 26.60 Calculates price. For more information on percentages, refer to chapter 3, Business Percentages.
Multiply 17, 22, and 25 by 7, storing ‘× 7’ as a constant operation. Table 1-8 Storing ‘x 7’ as a constant Keys JjPjª 4 GG4 GV4 Display 7.00 Description Stores ‘× 7’ as a constant operation. 119.00 Multiplies 17 × 7. 154.00 Multiplies 22 × 7. 175.00 Multiplies 25 × 7. Keys Display Description VJd\wG M vG 519.00 Stores 519 in register 2. Store 519 in register 2, then recall it. Table 1-9 Storing and recalling 0.00 519.00 Clears display. Recalls register 2. Store 1.
Time Value of Money (TVM) Enter any four of the five values and solve for the fifth. A negative sign in the display represents money paid out, and money received is positive. Table 1-11 Keys for TVM calculations Keys Description ]OJ Ù \Ú Ò Ï Ì É \¯ \Í Clears TVM memory and the current P_YR is displayed. Number of payments. Multiplies a value by the number of payments per year and stores as N. Interest per year. Present value. Payment. Future value. Begin or End mode. Number of payments per year mode.
Table 1-12 Calculating the monthly payment Keys :É Ì Display 0.00 -122.86 Description Enters future value. Calculates payment if paid at end of period. TVM What if... It is not necessary to reenter TVM values for each example. Using the values you just entered, how much can you borrow if you want a payment of 100.00? Table 1-13 Calculating a new payment Keys Display Description J::yÌ -100.00 Enters new payment amount. (Money paid out is negative). Ï 11,395.08 Calculates amount you can borrow. .
Amortization After calculating a payment using Time Value of Money (TVM), input the periods to amortize \Ê. Press \Ê once for periods 1-12, and once again for payments 1324. Press 4 to continually cycle through the principal, interest, and balance values (indicated and press by the PRIN, INT, and BAL annunciators respectively). Using the previous TVM example, amortize a single payment and then a range of payments. Amortize the 20th payment of the loan.
Table 1-16 Amortization example Keys Display Description 4 4 -1,388.36 Displays interest. 13,836.22 Displays the balance amount. For more information on amortization, refer to the section titled, Amortization in chapter 6, Time Value of Money Calculations. Depreciation Table 1-17 Depreciation keys Keys Description Ù Ò Ï É ]{ ]x ]u Expected useful life of the asset. Declining balance factor entered as a percentage. Depreciable cost of the asset at acquisition. Salvage value of the asset.
Table 1-18 Calculating the depreciation Keys Display \« G]{ \« Description 7,600.00 Remaining depreciable value after year one. 1,900.00 Depreciation of the asset in year two. 5,700.00 Remaining depreciable value after year two. For more information on depreciation, refer to chapter 7, Depreciation. Interest Rate Conversion To convert between nominal and effective interest rates, enter the known rate and the number of periods per year, then solve for the unknown rate.
Cash Flows, IRR/YR, NPV, and NFV Table 1-21 Cash flows, IRR, NPV, and NFV keys Keys Description ]O: \Í Clears cash flow memory. Number of periods per year (default is 12). For annual cash flows, P/YR should be set to 1; for monthly cash flows, use the default setting, 12. ¤ Cash flows, up to 45. “J” identifies the cash flow number. When preceded by a number, pressing ¤ enters a cash flow amount. number1 Æ number 2 ¤ Enter a cash flow amount, followed by Æ.
If you have an initial cash outflow of 40,000, followed by monthly cash inflows of 4,700, 7,000, 7,000, and 23,000, what is the IRR/YR? What is the IRR per month? Table 1-22 Calculating the IRR/YR and IRR per month Keys Display ]O: CFLO CLR Description Clears cash flow memory. (message flashes, then disappears) JG\Í Y::::y¤ Yj::¤ j:::ÆG¤ 12.00 -40,000.00 Sets payments per year. Enters initial outflow. (CF 0 flashes, then disappears) 4,700.00 Enters first cash flow.
Table 1-23 Calculating NPV and NFV Keys Display Description \½\« 643.88 Calculates NFV. For more information on cash flows, refer to chapter 8, Cash Flow Calculations in the HP 10bII+ Financial Calculator User’s Guide. Date and Calendar Table 1-24 Keys used for dates and calendar functions Keys Description ]È Enters dates in DD.MMYYYY or MM.DDYYYY formats. D.MY is the default. Numbers at the far right of a calculated date indicate days of the week. 1 is for Monday; 7 is for Sunday.
Bonds Bond calculations, primarily calculating bond price and yield, are performed by two keys, ]Ñ and ]Ô. These keys permit you to input data or return results. Pressing ]Û only calculates a result. The other keys used in bond calculations only permit you to input the data required for the calculations. Table 1-26 Bond calculation keys Keys Description ]Oj ]Û ]Ô ]Ñ ]Î ]Ë Clears bond memory. Calculates accrued interest only. Yield% to maturity or yield% to call date for given price. Price per 100.
Table 1-27 Bond calculation Keys ]Oj Y7GgG:J: ]¾ S7:YG:G: ]° S7jV]Î J::]Ë Y7jV]Ô ]Ñ 1]Û 4 Display BOND CLR (message Description Clears bond memory. flashes, then disappears) 4-28-2010 3 Inputs the settlement date (mm.ddyyyy format). 6-4-2020 4 6.75 100.00 Inputs the maturity date. Inputs CPN%. Inputs call value. Optional, as default is 100. 4.75 115.89 2.69 Inputs Yield%. Calculates the price. Displays the current value for accrued interest. 118.
Break-even Table 1-28 Break-even keys Keys Description ]OY ]¬ ]© ]¦ ]£ ]~ Clears break-even memory. Stores the quantity of units required for a given profit or calculates it. Stores the sales price per unit or calculates it. Stores variable cost per unit for manufacturing or calculates it. Stores the fixed cost to develop and market or calculates it. Stores the expected profit or calculates it. The sale price of an item is 300.00, the cost 250.00, and fixed cost 150,000.00. For a profit of 10,000.
Statistical Calculations Table 1-30 Statistics keys Keys Description \t Clear statistical registers. Enter one-variable statistical x-data ¡ data. Delete one-variable statistical x-data \¢ data. Enter two-variable statistical x-data Æ y-data ¡ data. Delete two-variable statistical Æ y-data \¢ v¡ \k \« \T \« \h \« \e \« data. x-data Opens editor for reviewing/ editing entered statistical data. Means of x and y. Mean of x weighted by y. Also calculates b, intercept.
Using the following data, find the means of x and y, the sample standard deviations of x and y, and the y-intercept and the slope of the linear regression forecast line. Then, use summation statistics to find Σ xy. x-data 2 4 6 y-data 50 90 160 Table 1-31 Statistics example Keys \t GÆV:¡ YÆd:¡ SÆJS:¡ v¡ Display Description 0.00 Clears statistics registers. 1.00 Enters first x,y pair. 2.00 Enters second x,y pair. 3.00 Enters third x,y pair. 1 2.
Probability Table 1-32 Probability keys Keys Description ]F ]o F ]I Calculates a cumulative normal probability given a Z-value. Calculates a Z-value given a cumulative normal probability. Calculates the cumulative Student’s T probability given degrees of freedom and a T-value. ]o I ]< ]9 ]E Calculates a T-value given degrees of freedom and the cumulative Student’s T probability. Calculates number of permutations of n items taken r at a time. Calculates number of combinations of n taken r at a time.
Trigonometric Functions Table 1-34 Trigonometry keys Keys Description Calculates sine, cosine, and tangent. ] c, R, or C Calculates inverse sine, inverse cosine, ]o and inverse tangent. c, R, or C Calculates hyperbolic sine, cosine and ]r tangent. c, R, or C ]ro Calculates inverse hyperbolic sine, cosine, and tangent. c, R, or C ]3 Toggles between radians and degrees modes. Degrees is the default setting. Find Sin θ =.62 in degrees. If RAD is displayed, press ]3.
Convert the results to radians using Pi. Table 1-36 Converting to radians Keys P\;aJg :4 Display .67 Description Converts degrees to radians. For more information on trigonometric functions, refer to chapter 2, Getting Started. At a Glance...
22 At a Glance...
2 Getting Started Power On and Off =. To turn the calculator off, press the orange shift key, \, then >. To change the brightness of the display, hold down = and then simultaneously press 1 or A. To turn on your HP 10bII+, press Since the calculator has continuous memory, turning it off does not affect the information you have stored. To conserve energy, the calculator turns itself off after five minutes of inactivity. The calculator uses two CR2032 coin batteries.
Basics of Key Functions Table 2-1 Basics of key functions Keys = ][blue] \[orange] JGD| ]3 M \t \N ]Oj ]OY ]OJ ]O: \> 24 Getting Started Display 0.00 Description Turns calculator on. 0.00 Displays shift annunciator . Displays shift annunciator . 0.00 12_ Erases last character. RAD Toggles between radians and degrees. The item before the / is the alternate; the item after the / is the default setting.
Shift Keys Most keys on the HP 10bII+ have three functions: • a primary function printed in white on the key. • a secondary function printed in orange on the bevel of the key. • a tertiary function printed in blue above the key on the keyboard (see Figure 1). Figure 1 \ or ], a shift annunciator or is displayed to indicate that the shifted functions are active. For example, press \ followed by 2 to multiply a number in the display by itself. To turn the shift annunciators off, press \ or ] again.
Table 2-2 Clearing functions Keys Associated Function ]OY ]OJ ]O: Clears break-even memory. Clears TVM memory. Clears cash flow memory. Simple Arithmetic Calculations Operating Modes To change the operating mode, press the blue shift key, ] followed by ? to toggle between Algebraic and Chain modes. A brief message is displayed indicating the selected operating mode. To view the current mode, press v]?. The current mode will flash, then disappear.
If you press an operator key after completing a calculation, the calculation is continued. Table 2-5 Continuing a calculation Keys Display Description 1JJV7V4 356.42 Completes calculation of 240.92 + 115.5. Calculations in Chain Mode Calculations in Chain mode are interpreted in the order in which they are entered. For example, entering the following numbers and operations as written from left to right, J1GPD4, returns 9.
For example, to calculate 1 + (2 x 3), you may enter the problem as written from left to right, with parentheses to prioritize the multiplication operation. When entered with parentheses, this expression returns a result of 7. Calculations in Algebraic Mode In Algebraic mode, multiplication and division have a higher priority than addition and subtraction. For example, in Algebraic mode, pressing J1GPD4 returns a result of 7.00. In Chain mode, the same key presses return a result of 9.00.
Table 2-8 Using parentheses in calculations Keys Display P d4 Description 0.41 Calculates 30 ÷ 73. 3.70 Multiplies the result by 9. Negative Numbers Enter the number and press y to change the sign. Calculate -75 ÷ 3. Table 2-9 Changing the sign of numbers Keys Display Description jVy aD4 -75_ Changes the sign of 75. –25.00 Calculates result. Understanding the Display and Keyboard Cursor The blinking cursor ( _ ) is visible when you are entering a number.
Table 2-10 Clear memory keys Keys Description ]Oj ]OY ]OJ ]O: \t Clears bond memory. Clears break-even memory. Clears TVM memory. Clears cash flow memory. Clears statistics memory. Clear All \N all clears all memory in the calculator, with the exception of the payments per year (P/Yr) setting. To clear all memory and reset calculator modes, press and hold down =, then press and hold down both Ù and Ï. When you release all three, all memory is cleared. The All Clear message is displayed.
Table 2-11 Annunciators and status Annunciator Status , A shift key has been pressed. When another key is pressed, the functions labeled in orange or blue are executed. INV Inverse mode is active for trigonometric or probability functions. RAD Radians mode is active. BEG Begin mode is active; payments are at the beginning of a period. D.MY Day-month-year date format (DD.MMYYYY) is active. 360 360-day calendar is active. SEMI Semi-annual coupon payment schedule (bonds) is active.
Table 2-11 Annunciators and status Annunciator Status FUNC A math error has occurred (for example, division by zero). Input Key Æ key is used to separate two numbers when using two-number functions or twovariable statistics. The Æ key can also be used to enter cash flows and cash flow counts, The ordered pairs, and evaluate any pending arithmetic operations, in which case the result is the same as pressing 4.
Table 2-12 Statistics keys Keys Description ]U ]X Sum of the y-values. Sum of the x-values. Time Value of Money (TVM), Cash Flows, Bond, and Break-even Keys When entering data for TVM, cash flows, bond, depreciation and break-even calculations, results are calculated based on data entered into specific memory registers. When pressed, the keys used for these operations: • • store data. enter data for a variable that is used during calculations (input only).
Table 2-14 One-number functions Keys Description § \} \b \B \2 \K \H \E ] Divide a number by 100. Rounds x to the number specified by the display format. Calculates 1/x. Calculates the square root of x. Calculates the square of x. Calculates natural exponent to the power of x. Calculates natural log. Calculates factorial of n (where -253 < n < 253). The Gamma function is used to calculate n! for non-integers or negative numbers. Calculates sine, cosine, or tangent.
Trigonometric and Hyperbolic Functions and Modes Selecting Angle Format The trigonometric angle format determines how numbers are interpreted when using trigonometry functions. The default format for angles on the 10bII+ is degrees. To change to radians mode, press ]3. When radians mode is active, the RAD annunciator is displayed. Trigonometric Functions Table 2-15 Trigonometric functions Keys Description ]c ]R ]C ]oc ]oR ]oC Calculates sine, written as sin. Calculates cosine, written as cos.
Table 2-16 Example using various trigonometric calculations Keys Display Description A7SG]oR 4 \5G 51.6839 Displays inverse cosine of 0.62. 17.8288 Calculates arccos 0.35 - arccos 0.62. 17.83 Return display to default format. Pi Pressing \; displays the value of π . Although the displayed value is appears in the current display format, the 12 digit value is actually used for calculations. π is often used during calculations in radians mode, as there are 2 π radians in a circle.
Example Perform the following hyperbolic calculations. Table 2-19 Example performing various hyperbolic calculations Keys Display Description \5Y J7GV]rc 17Vd]rC 4 ]roR \5G 0.0000 Sets display to four decimal places. 1.6019 Display sinh 1.25. 0.5299 Displays tanh 0.59. 2.1318 Calculates sinh 1.25 + tanh 0.59. 1.3899 Calculates acosh 2.1318. 1.39 Returns display to default format.
Table 2-20 Example calculating percent change as an in-line function Keys Jj\¨ Gd 4 Press Display 17.00 29_ 70.59 Description Enters number1, displays the PEND annunciator indicating the calculator is awaiting instructions. Enters number 2. Calculates the percent change. M, and now calculate the same example using the Æ key to store the first number, then key in the second number and perform the operation. Table 2-21 Example calculating percent change using ‘INPUT’ Keys Display Description JjÆ 17.
The Table 2-23 below lists the two-number functions of the calculator. Table 2-23 Two-number functions Keys Description 1APa \Q \¨ ]9 ]< \Ç Addition, subtraction, multiplication, division. The power function. % Change. Combinations. Permutations. The date and day, past or future, that is a given number of days from a given date. \Ä ]I The number of days between two dates. ]oI Calculates a t-value given degrees of freedom and the cumulative Student’s t probability.
Table 2-24 Calculating the expression Keys 1Yj7G1 J7J\2 4 Display Description 51.67 Calculates 1.21 Calculates 1.12. 52.88 20 + 47.20. Completes the calculation. Example 2 Calculate natural logarithm (e2.5). Then calculate 790 + 4! Table 2-25 Calculating the logarithm value Keys Display G7V\K \H jd:1Y\E 4 Description 12.18 Calculates e2.5. 2.50 Calculates natural logarithm of the result. 24.00 Calculates 4 factorial. 814.00 Completes calculation.
Last Answer When a calculation is completed by pressing 4, or a calculation is completed during another operation, the result is stored in a memory location that contains the last calculated result. This enables the last result of a calculation to be used during the next calculation. To access the last calculated answer, press v4. Unlike the other stored memory registers however, this register is automatically updated when you complete a calculation.
Regardless of the current display format, each number is stored internally as a signed, 12-digit number with a signed, three-digit exponent. Specifying Displayed Decimal Places To specify the number of displayed decimal places: 1. 2. \5 followed by :–d for the desired decimal setting. \5 followed by 7, v, or s changes the display mode. Pressing \7 provides the best estimate and displays as many digits as required. v is the value for 10, and s for 11.
Table 2-30 Example displaying all digits Keys Display Jaj4 \54 1.43 142857142857 Description Divides. Displays all 12 digits. Scientific Notation Scientific notation is used to represent numbers that are too large or too small to fit in the display. For example, if you enter the number 10,000,000 x 10,000,000 =, the result is 1.00E14, which means one times ten to the fourteenth power, or 1.00 with the decimal point moved fourteen places to the right. You can enter this number by pressing J\ zJY.
Table 2-31 Example displaying rounding off numbers Keys d7gjSVYD GJ \5G \54 (while you press 4). \} Display 9.87654321_ Description Enters a number with more than two nonzero decimal places. 9.88 Displays two decimal places. 987654321000 Displays all digits without the decimal. 9.88 Rounds to two decimal places (specified by pressing \5G). \54 988000000000 Shows rounded, stored number.
3 Business Percentages The Business Percentage Keys When entering data for business percentage calculations, results are calculated based on data entered into specific memory registers. When pressed, the keys used for these operations: • • • store data. enter known data for variables used during calculations. calculate unknown variables based on stored data. You can use the 10bII+ to calculate simple percent, percent change, cost, price, margin, and markup.
Table 3-2 Subtracting a percent in a calculation Keys Display Description G::A GV§ 4 200.00 Enters 200. 50.00 Multiplies 200 by 0.25 and subtracts 50 from 200. 150.00 Completes the calculation. Example 2 You borrow 1,250 from a relative, and you agree to repay the loan in a year with 7% simple interest. How much money will you owe? Table 3-3 Adding a percent in a calculation Keys JGV:1j§ 4 Display 1,337.50 Description Calculates loan interest, 87.50 and adds 87.50 and 1250.
Margin and Markup Calculations The 10bII+ can calculate cost, selling price, margin, or markup. Table 3-6 Keys for margin and markup Application Margin Markup Keys Description À, ¼, ® À, ¼, Ã Margin is markup expressed as a percent of price. Markup calculations are expressed as a percent of cost. v and then the key you wish to see. For example, to see the value stored as À, press vÀ.
Table 3-8 Calculating the retail price Keys Display Description ¼ 30.40 Calculates retail price. Using Margin and Markup Together Example A food cooperative buys cases of canned soup with an invoice cost of 9.60 per case. If the co-op routinely uses a 15% markup, for what price should it sell a case of soup? What is the margin? Table 3-9 Calculating the margin Keys d7SÀ JVÃ ¼ ® 48 Business Percentages Display Description 9.60 Stores invoice cost. 15.00 Stores markup. 11.
4 Number Storage and Storage Register Arithmetic Using Stored Numbers in Calculations You can store numbers for reuse in several different ways: • • ª (Constant) to store a number and its operator for repetitive operations. Use 3 Key Memory (s, p, and m) to store, recall, and sum numbers with a single Use keystroke. • Use \w and v to store to, and recall from, the 20 numbered registers. Using Constants ª to store a number and arithmetic operator for repetitive calculations.
Example 2 Calculate 10 + 10%, 11 + 10%, and 25 + 10%. Table 4-2 Storing ‘+ 10%’ as a constant Keys J:1J:§ª 4 4 GV4 Display Description 1.00 Stores + 10% as a constant. 11.00 Adds 10% to 10. 12.10 Adds 10% to 11. 27.50 Adds 10% to 25. Example 3 Calculate 23 and 43. Table 4-3 Storing ‘y3’ as a constant Keys G\QDª 4 Y4 50 Number Storage and Storage Register Arithmetic Display Description 3.00 Stores y3 as constant. 8.00 Calculates 23. 64.00 Calculates 43.
Example 4 Calculate the percent change between 55 and 32 and store it as a constant. Then calculate the percent change between 50 and 32, and 45 and 32. Table 4-4 Calculating percent change Keys Display Description VV\¨DGª 4 V:4 YV4 32.00 Stores % change 32 as constant. -41.82 Calculates the % change between 55 and 32. -36.00 Calculates the % change between 50 and 32. -28.89 Calculates the % change between 45 and 32.
Example Use the M register to add 17, 14.25, and 16.95. Then subtract 4.65 and recall the result. Table 4-6 Calculating basic arithmetic operations using M register Keys Display Jjs JY7GVm JS7dVm Y7SVym p Description 17.00 Stores 17 in M register. 14.25 Adds 14.25 to M register. 16.95 Adds 16.95 to M register. -4.65 Adds -4.65 to M register. 43.55 Recalls contents of the M register. Using Numbered Registers \w and v keys access the 20 user registers, designated 0-19.
Table 4-7 Calculating the expression using two storage registers Keys Display Description YjV7S \w7Y aDd7JV \wG 4 VS:7J1 v7Y 475.60 Stores 475.60 (displayed number) in R14. 39.15 Stores 39.15 in R2. 12.15 Completes first calculation. 1,035.70 Recalls R14. NOTE: If the calculator is set for Algebraic mode, press 4 at the end of this step. avG 4 39.15 Recalls R2. 26.45 Completes second calculation.
Table 4-8 Keys for performing arithmetic inside registers Keys New Number in Register \wa register number Old contents ÷ displayed number. Example 1 Store 45.7 in R3, multiply by 2.5, and store the result in R3. Table 4-9 Calculating and storing the result in the storage register Keys Display Description YV7j \wD G7V \wPD vD 45.70 Stores 45.7 in R3. 2.50 Multiplies 45.7 in R3 by 2.5 and stores result (114.25) in R3. 114.25 Displays R3. Example 2 Store 1.
5 Picturing Financial Problems How to approach a Financial Problem The financial vocabulary of the HP 10bII+ is simplified to apply to all financial fields. For example, your profession may use the term balance, balloon payment, residual, maturity value, or remaining amount to designate a value that the HP 10bII+ knows as É (future value). The simplified terminology of the HP 10bII+ is based on cash flow diagrams. Cash flow diagrams are pictures of financial problems that show cash flows over time.
Signs of Cash Flows In cash flow diagrams, money invested is shown as negative and money withdrawn is shown as positive. Cash flowing out is negative, cash flowing in is positive. For example, from the lender’s perspective, cash flows to customers for loans are represented as negative. Likewise, when a lender receives money from customers, cash flows are represented as positive. In contrast, from the borrower’s perspective, cash borrowed is positive while cash paid back is negative.
Compound Interest A compound-interest contract is like a series of simple-interest contracts that are connected. The length of each simple-interest contract is equal to one compounding period. At the end of each period the interest earned on each simple-interest contract is added to the principal. For example, if you deposit 1,000.
• As a periodic rate. This is the rate that is applied to your money from period to period. • As an annual nominal rate. This is the periodic rate multiplied by the number of periods in a year. • As an annual effective rate. This is an annual rate that considers compounding. In the previous example of a 1,000.00 savings account, the periodic rate is 1/2 % (per month), quoted as an annual nominal rate of 6% ( 1/2 × 12).
Figure 4 Cash flow diagram (Borrower’s perspective) One of the values for PV, PMT, FV can be zero. For example, following is a cash flow diagram (from the saver’s perspective) for a savings account with a single deposit and a single withdrawal five years later. Interest compounds monthly. In this example, PMT is zero. Figure 5 Cash flow diagram (Saving perspective) Time value of money calculations are described in the next chapter titled, Time Value of Money Calculations.
The following is a cash flow diagram for an investment in a mutual fund. This is an example of a problem that is solved using either \½ (Net Present Value) or \Á (Internal Rate of Return per Year). Figure 6 Cash flow diagram (Investment in a mutual fund) Cash flow problems are described in chapter 8 titled, Cash Flow Calculations.
6 Time Value of Money Calculations Using the TVM Application The time value of money (TVM) application is used for compound interest calculations that involve regular, uniform cash flows – called payments. Once the values are entered you can vary one value at a time, without entering all the values again. To use TVM, several prerequisites must be met: • The amount of each payment must be the same. If the payment amounts vary, use the procedures described in chapter 8 titled, Cash Flow Calculations.
Table 6-1 Keys for performing TVM calculations Keys Stores or Calculates \¯ \Ê Switches between Begin and End mode. In Begin mode, the BEGIN annunciator is displayed. Calculates an amortization table. vÙ, vÒ, vÏ, vÌ, and vÉ. Pressing v\Ú recalls the total number of payments in years and v\Í To verify values, press shows you the number of payments per year. Recalling these numbers does not change the content of the registers.
Figure 7 Cash flow diagram (Calculate PMT) Set to End mode. Press \¯ if BEGIN annunciator is displayed. Table 6-2 Calculating the monthly payment Keys JG\Í DPJGÙ J:7VÒ JYV::A JV::Ï :É Ì Display Description 12.00 Sets periods per year (optional, as 12 is the default). 36.00 Stores number of periods in loan. 10.50 Stores annual nominal interest rate. 13,000.00 Stores amount borrowed. 0.00 Stores the amount left to pay after 3 years. -422.53 Calculates the monthly payment.
Table 6-3 Calculating the interest rate Keys Display Description 1V:Ì Ò -372.53 Decreases payment from 422.53. 2.03 Calculates annual interest rate for the reduced payment. Part 3 If interest is 10.5%, what is the maximum you can spend on the car to lower your car payment to 375.00? Table 6-4 Calculating the amount Keys Display Description J:7VÒ DjVyÌ Ï 1JV::4 10.50 Stores original interest rate. -375.00 Stores desired payment. 11,537.59 Calculates amount of money to finance. 13,037.
Set to End mode. Press \¯ if BEGIN annunciator is displayed. Table 6-5 Calculating the maximum purchase price Keys JG\Í D:\Ú :É j7VÒ dD:yÌ Ï 1JG:::4 Display Description 12.00 Sets periods per year. 360.00 Stores the length of the mortgage (30 × 12). 0.00 Pays mortgage off in 30 years. 7.50 Stores interest rate. -930.00 Stores desired payment (money paid out is negative). 133,006.39 Calculates the loan you can afford with a 930 payment. 145,006.
Figure 9 Cash flow diagram (Calculate PMT) Set to End mode. Press \¯ if BEGIN annunciator is displayed. Table 6-6 Calculating the monthly payment Keys JG\Í GV\Ú :É JjGV::Ï g7gÒ Ì Display 12.00 300.00 Description Sets periods per year. Stores length of mortgage (25 × 12 = 300 months). 0.00 Stores loan balance after 25 years. 172,500.00 Stores original loan balance. 8.80 -1,424.06 Stores annual interest rate. Calculates the monthly payment.
Figure 10 Cash flow diagram (Calculate FV) The value in PMT should always be rounded to two decimal places when calculating FV or PV to avoid small, accumulative discrepancies between non-rounded numbers and actual (dollars and cents) payments. If the display is not set to two decimal places, press \5G. Table 6-7 Calculating the final amount Keys \}Ì YgÙ É 1vÌ4 Display -1,424.06 Description Rounds payment to two decimal places, then stores. 48.
Figure 11 Cash flow diagram (Calculate the number of years) Since this account has no regular payments (PMT = 0), the payment mode (End or Begin) is irrelevant. Table 6-8 Calculating the number of years Keys ]OJ J\Í G:::yÏ D:::É j7GÒ Ù Display Description 0.00 Clears TVM memory. 1.00 Sets P/YR to 1 since interest is compounded annually. -2,000.00 Stores amount paid out for the first deposit. 3,000.00 Stores the amount you wish to accumulate. 7.20 Stores annual interest rate. 5.
Table 6-9 Calculating the balance after six years Keys Display SÙ É 6.00 3,035.28 Description Sets n to 6 years. Calculates the amount you can withdraw after six years. Example: An Individual Retirement Account You opened an individual retirement account on April 14, 1995, with a deposit of 2,000. 80.00 is deducted from your paycheck and you are paid twice a month. The account pays 6.3% annual interest compounded semimonthly.
Table 6-10 Calculating the balance amount Keys Display S7DÒ JV\Ú É 6.30 360.00 52,975.60 Description Stores interest rate. Stores the number of deposits. Calculates the balance amount. Example: An Annuity Account You opt for an early retirement after a successful business career. You have accumulated a savings of 400,000 that earns an average of 7% annual interest, compounded monthly.
Lease Calculations A lease is a loan of valuable property (like real estate, automobiles, or equipment) for a specific amount of time, in exchange for regular payments. Some leases are written as purchase agreements, with an option to buy at the end of the lease (sometimes for as little as 1.00). The defined future value (FV) of the property at the end of a lease is sometimes called the residual value or buy out value. All five TVM application keys can be used in lease calculations.
Table 6-12 Calculating the monthly lease payment Keys Display JG\Í J:Ò JDV::yÏ jV::É DSÙ Ì Description 12.00 Sets payments per year. 10.00 Stores desired annual yield. -13,500.00 7,500.00 Stores lease price. Stores residual (buy out value). 36.00 Stores length of lease, in months. 253.99 Calculates the monthly lease payment.
This solution requires four steps: 1. Calculate the present value of the 47 monthly payments: (4 × 12) - 1 = 47. 2. Add the value of the additional advance payment. 3. Find the present value of the buy option. 4. Sum the values calculated in steps 2 and 3. Step 1 Find the present value of the monthly payments. Set to Begin mode. Press \¯ if BEGIN annunciator is not displayed. Table 6-13 Calculating the present value Keys JG\Í YjÙ GY::yÌ :É dÒ Ï Display Description 12.00 Sets payments per year. 47.
Table 6-15 Calculating the present value of the last cash flow Keys Display :Ì JV:::yÉ Ï 0.00 Description Stores zero payment for this step of solution. -15,000.00 Stores value to discount. 10,479.21 Calculates the present value of last cash flow. Step 4 Add the results of ’Step 2’ and ’Step 3’. Table 6-16 Calculating the present value of lease Keys 1p4 Display 108,356.77 Description Calculates the present (capitalized) value of lease. (Rounding discrepancies are explained on page 67.
The AMORT key on the HP 10bII+ allows you to calculate. The • The amount applied to interest in a range of payments. • The amount applied to principal in a range of payments. • The loan balance after a specified number of payments are made. \Ê function assumes you have just calculated a payment or you have stored the appropriate amortization values in I/YR, PV, FV, PMT, and P/YR. Table 6-17 Keys for storing the amortization values Keys Description Ò Ï É Ì \Í Annual nominal interest rate.
If you store, recall, or perform any other calculations during amortization, pressing 4 will no longer cycle through interest, principal, and balance. To resume amortization with the same set of periods, press v\Ê. Example: Amortizing a Range of Payments Calculate the first two years of the annual amortization schedule for a 30 year, 180,000 mortgage, at 7.75% annual interest with monthly payments. Set to End mode. Press \¯ if BEGIN annunciator is displayed.
The amount paid toward interest and principal (13,894.67 + 1,579.84 = 15,474.51) equals the total of 12 monthly payments (12 × 1,289.54 = 15,474.51). The remaining balance equals the initial mortgage, less the amount applied toward principal (180,000 - 1,579.84 = 178,420.16). Amortize the second year: Table 6-20 Calculating the remaining balance Keys Display Description JDÆGY \Ê 4 4 4 13 – 24 Displays PER and the next range of periods. -1,706.
Table 6-21 Calculating the monthly payment Keys Display Description Ì -310.42 Calculates the monthly payment. Amortize the 1st, 25th, and 54th payments Table 6-22 Calculating the amount Keys JÆ \Ê 4 4 4 GVÆ \Ê 4 4 4 VYÆ \Ê 4 4 4 78 Time Value of Money Calculations Display Description 1.00 Enters first payment. 1–1 Displays PER and the amortized payment period. -310.42 0.00 13,939.58 25.00 Displays PRIN and the first principal payment. Displays INT and the interest.
Interest Rate Conversions The Interest Conversion application uses three keys: \Ó, \Ð, and \Í. They convert between nominal and annual effective interest rates. If you know an annual nominal interest rate and you wish to solve for the corresponding annual effective rate: 1. Enter the nominal rate and press \Ó. 2. Enter the number of compounding periods and press 3. Calculate the effective rate by pressing \Í. \Ð. To calculate a nominal rate from a known effective rate: 1.
Table 6-23 Calculating the interest rate (First bank) Keys \Ð Display 6.87 Description Calculates the annual effective rate. Second Bank Table 6-24 Calculating the interest rate (Second bank) Keys Display S7SV\Ó JG\Í \Ð Description 6.65 Stores nominal rate. 12.00 Stores monthly compounding periods. 6.86 Calculates the annual effective rate. Third Bank Table 6-25 Calculating the interest rate (Third bank) Keys S7SD\Ó DS:\Í \Ð Display 6.63 360.00 6.85 Description Stores nominal rate.
Example: Monthly Payments, Daily Compounding Starting today, you make monthly deposits of 25 to an account paying 5% interest, compounded daily (using a 365 day year). What will the balance be in seven years? Step 1 Calculate the equivalent rate with monthly compounding. Table 6-26 Calculating the equivalent nominal percentage rate Keys Display V\Ó DSV\Í \Ð JG\Í \Ó 5.00 365.00 5.13 Description Stores nominal percentage rate. Stores bank’s compounding periods per year. Calculates annual effective rate.
Resetting the TVM Keys Press ]OJ to clear the TVM registers. This sets N, I/YR, PV, PMT, and FV to zero and briefly displays TVM CLR, followed by the current value in P/Yr.
7 Depreciation On the 10bII+, depreciation calculations are performed using the functions printed in blue on the keyboard located under the blue bracket titled, DEPRECIATION. Depreciation calculations are based on data entered into the Time Value of Money (TVM) keys: Ï, É, Ò, and Ù. Table 7-1 Depreciation keys TVM Key Description ]OJ Ù Ï É ]{ Clear TVM memory. Since the TVM and depreciation applications share the same memory, clearing TVM resets depreciation also.
To perform a depreciation calculation: 1. Enter the original cost of the asset, using Ï. 2. Enter the salvage value of the asset, using FV. If the salvage value is zero, press :É. 3. Enter the expected useful life of the asset (in years), followed by Ù. 4. If the declining-balance method is being used, enter the declining-balance factor (as a Ò percentage), followed by . For example, 1-1/4 times the straight-line rate — 125 percent declining-balance — would be entered as 125. 5.
Table 7-2 Depreciation example using SL Keys Display VÙ J]{ Description 5.00 Inputs 5 for the expected useful life of the asset in the selected format. 1,900.00 Enters the year for which depreciation is to be calculated and calculates the depreciation of the asset in year one. TVM and X are displayed. \« 7,600.00 Displays remaining depreciable value after year one. X changes to Y in the display. G]{ 1,900.
Example 3 A machine was purchased for 5,000 and is to be depreciated over seven years with no salvage value. Using the double declining balance method, what is the depreciation for the first three years of the machine's life? What is the remaining depreciable value? Table 7-4 Depreciation example using Declining Balance Keys Display ]OJ V:::Ï jÙ G::Ò :É J]u G]u D]u \« TVM CLR (message flashes then disappears) Description Clears TVM registers. 5,000.
8 Cash Flow Calculations How to Use the Cash Flow Application The cash flow application is used to solve problems where cash flows occur over regular intervals. Problems with regular, equal, periodic cash flows are handled more easily using the TVM keys. To operate the cash flow system, cash flow amounts and repeat values are keyed in either individually or together. In the following chapter, the term repeat value is used to describe the number of times a cash flow occurs.
Table 8-1 Cash Flow Keys Key Description ]O: \Í number1 ¤ Clears cash flow memory. Æ number 2 ¤ number1 \¥ v¤ number 2 Number of periods per year (default is 12). For annual cash flows, P/YR should be set to 1; for monthly cash flows, use the default setting, 12. Cash flows, up to 45. J identifies the cash flow number. When preceded by a ¤ enters a cash flow amount. Enter a cash flow amount, followed by Æ. Enter a number for the repeat value followed by ¤.
Figure 1 As illustrated in Figure 1, if no more than 15 data points are stored in the statistics memory, you may store up to 45 cash flows with the shared memory space. If more than 15 data points are stored in the statistics memory, the total memory available for storing cash flows is reduced. For example, in Figure 2, there are 25 data points stored, and the amount of available shared memory has therefore decreased by 10 slots.
Calculating Internal Rate of Return 1. 2. 3. ]O:, and store the desired number of periods per year in P/YR. Enter the cash flows using Æ and ¤. Press \Á. Press Figure 4 Cash flow diagram (Investments in stock) Table 8-2 Example 1: a short term investment Keys ]O: JG\Í V:::y¤ G:::y¤ 90 Cash Flow Calculations Display CFLO CLR Description Clears cash flow memory. (message flashes, then disappears) 12.00 -5,000.00 (CF 0 flashes, then disappears) -2,000.
Table 8-2 Example 1: a short term investment Keys Y:::y¤ JJjSV7Gd¤ \Á aJG Display -4,000.00 (CF 2 flashes, then disappears) 11,765.29 (CF 3 flashes, then disappears) 38.98 3.25 Description Enters second cash flow. Note the CFLO and CF annunciators. Enters third cash flow. Note the CFLO and CF annunciators. Calculates annual nominal yield. Monthly yield.
Figure 5 Initial cash flow and cash flow groups Whenever you enter a series of cash flows, it is important to account for every period on the cash flow diagram, even periods with cash flows of zero. Example Enter the cash flows from the preceding diagram and calculate the IRR/YR. Assume there are 12 periods per year. Table 8-3 Example calculating IRR and effective interest rate Keys ]O: JG\Í JJ:::y¤ :¤ S\¥ 92 Cash Flow Calculations Display CFLO CLR Description Clears cash flow memory.
Table 8-3 Example calculating IRR and effective interest rate Keys Display J:::¤ D\¥ J::::¤ 1,000.00 (CF 2 flashes, then disappears) 3.00 (CFn 2 flashes, then disappears) 10,000.00 (CF 3 flashes, then disappears) \Á 21.22 Description Enters second cash flow group amount. Note the CFLO and CF annunciators. Enters number of repetitions. Note the CFLO and N annunciators. Enters third cash flow. Note the CFLO and CF annunciators. Calculates the annual nominal yield.
6. To replace the currently displayed value, simply type a new number and press 7. Æ. Only valid entries are accepted. If you type an invalid entry, such as a value of 0 for the count, the ERROR annunciator appears and the value is rejected. To clear the current cash flow or repeat value without removing the entire pair, press |. If the cash flow amount is displayed, it will be set to a value of 0. If the cash flow repeat value is displayed, it will be set to a value of 1. 8.
Table 8-5 Editing cash flows Keys Display Description jV::Æ1GÆ 3 2.00 Inputs new cash flow amount and repeat value. Displays the new repeat value, 2.00, for CF3. 1JG::yÆ1G Æ ]X M \Á Inputs new cash flow, CF4, 4 is displayed first, with and repeat value. no value followed by 4 -1,200, then 4 2.00 3,600.00 Displays total of the cash flows. 0.00 Exit the editor. 58.97 Calculate the new annual yield.
How much should you pay for the contract if you wish to yield a yearly rate of 15% on your investment? Figure 6 Cash flow diagram (Calculate the amount) The following example uses the Æ and ¤ keys to enter the cash flow amount and repeat value simultaneously.
Keys :ÆY¤ jV::ÆJ¤ Display Description Input fifth cash flow amount and (CFn 4 flashes, then repeat value. disappears) 4.00 1.00 Input sixth cash flow amount and (CFn 5 flashes, then repeat value. disappears) :Æd¤ Input seventh cash flow amount and (CFn 6 flashes, then repeat value. disappears) J::::ÆJ¤ Input eighth cash flow amount and (CFn 7 flashes, then repeat value. disappears) 9.00 1.00 The cash flows that describe your prospective investment are now in the calculator. Press v¤.
Figure 7 Cash flow diagram (Calculates NPV) Automatic Storage of IRR/YR and NPV When you calculate NPV, the result is stored in PV for your convenience. To recall that result, vÏ. If you haven’t changed the TVM values from the last example using NPV, when you press vÏ the result is 27,199.92. When you calculate IRR/YR, the result is stored in I/YR. Press vÒ to display the annualized yield. More examples of NPV, NFV press and IRR/YR calculations can be found in the chapter 13 titled, Additional Examples.
9 Calendar Formats and Date Calculations Calendar Format The calendar options for bonds and date calculations are Actual (ACT) and 360. Press ]Å to toggle between these options. The default setting, Actual, is based on a 365day calendar. The alternate setting, 360, is based on a 360-day calendar. It is important to note date and bond calculations return different values for each of these settings, so verify the calendar mode is appropriate for your problem before you begin.
: through d that you wish to appear after the decimal point. To view the entire date, press S. For more information on changing the number 2. Enter the number of digits display, refer to the section titled, Specifying Displayed Decimal Places in chapter 2. To key in a date in M.DY format: 1. Key in one or two digits for the month. 2. Press 7. 3. Key in two digits for the day. 4. Key in four digits for the year. \Ç or \Ä to display the date in the selected number 5. Press either display format.
Date Calculations and Number of Days To calculate the date and day, past or future, that is a given number of days from a given date as an in-line function: 1. Key in the given date and press \Ç. 2. Key in the number of days. 3. If the other date is in the past, press 4. Press y. 4 to display the date in the selected number display format. To calculate the date and day, past or future, that is a given number of days from a given date using 1. Æ: Key in the given date and press Æ. 2.
Table 9-2 Date calculation example as an in-line function Keys Display JG7JgG:JJ \ÇJ::4 To enter the data for this example using the Description 12.182011_ Keys in the date in MM.DDYYYY format. 3-27-2012 2 Calculates the date. Æ key: Table 9-3 Date calculation example using the ‘INPUT’ key Keys Display JG7JgG:JJ ÆJ::\Ç Description 12.182011_ Keys in the date in MM.DDYYYY format. 3-27-2012 2 Returns the same results using the Æ key.
Table 9-4 Calculating the actual number of days as an in-line function Keys Display Description ]È 0.00 Sets the desired date format. Note the D.MY annunciator. ]Å 0.00 Sets the desired calendar format, in this case, actual days (optional if the 360 annunciator is not displayed, as Actual is the default). \5S 0.000000 Sets the number of displayed decimal places so the entire date is displayed (optional). Y7:SG:J:\Ä DJ7J:G:J: 4 4.062010 Inputs the starting date in the selected format. 149.
Using the Æ key: Table 9-6 Calculating the actual number of days using the ‘INPUT’ key Keys M J:7JjG:JGÆ S7:YG:JV\Ä 104 Calendar Formats and Date Calculations Display Description 0.00 Clear display. 10.17 Keys in the date in MM.DDYYYY format and displays digits in the selected display format (2). 960.00 Returns the same results.
10 Bonds The Bond Keys On the 10bII+, bond calculations are based on data or settings stored in the ten keys which make up the top two rows of the keyboard. The functions used in bond calculations are printed in blue above the keys on the keyboard. To access the bond functions, press ] followed by the desired function. See the table below for a description of the bond keys. Table 10-1 Bond keys Keys Description ]Oj ]Û ]Ô ]Ñ ]Î ]Ë ]È ]Å ]Â ]¾ ]° Clears bond memory. Calculates accrued interest only.
When entering data for bond calculations, results are calculated based on data entered into specific memory registers. When pressed, the keys used for these operations: • • • store data. enter data for variables used during calculations (input only). calculate unknown variables based on stored data. Most of the other keys used in bond calculations allow you to enter data for a variable, but you cannot solve for that variable. The exception is the ]Û key.
Table 10-2 Bond calculation example Keys S7:YG:G: ]° S7jV]Î J::]Ë Display 6-4-2020 4 6.75 100.00 Description Inputs June 4, 2020 for the maturity date. Inputs 6.75% for the value for CPN%. Inputs call value. Optional, as default is 100. Note: if Call requires another value, key in the number followed by ]Ë. Y7jV]Ô ]Ñ 1]Û 4 4.75 115.89 2.69 118.58 Inputs 4.75% for Yield%. Calculates the price. Displays the current value for accrued interest.
Table 10-3 Keys Display J:7JVG:G: ]° Y7JVG:JG ]¾ ]Ô 10-15-2020-4 4-15-2012-7 5.72 Description Inputs October 15, 2020 for the maturity date. Inputs April 15, 2012 for the settlement date. Calculates yield as a %. Continuing with the same bond problem, assume the bond will not be called. What is the expected yield to maturity? Table 10-4 Keys Display Description J::]Ë 100.00 Inputs new call value.
11 Break-even The break-even function allows you to study problems involving a profit, when a quantity of items, with a cost to manufacture and a fixed price to develop and market, is sold at a given price. On the 10bII+, break-even calculations are performed using the functions printed in blue on the keyboard located under the blue bracket titled, BREAKEVEN.
Example 1 The sale price of an item is 300.00, the cost is 250.00, and the fixed cost is 150,000.00. How many units would have to be sold to make a profit of 10,000.00? Table 11-2 Break-even example Keys ]OY JV::::]£ GV:]¦ D::]© J::::]~ ]¬ 110 Break-even Display BK EV CLR Description Clears break-even memory. (message flashes, then disappears) 150,000.00 Inputs fixed cost. 250.00 Inputs variable cost per unit. 300.00 Inputs price. 10,000.00 Inputs profit. 3,200.
Example 2 What is the estimated maximum fixed cost you can afford to manufacture 10,000 water filters, if your desired selling price is 45.00? Assume the cost per unit is 23.00. Since you want to calculate the maximum fixed cost, your profit for the purpose of the example will be 0.00. Table 11-3 Calculating the projected maximum fixed cost Keys ]OY J::::]¬ YV]© GD]¦ :]~ ]£ Display BK EV CLR Description Clears break-even memory. (message flashes, then disappears) 10,000.
Resetting the Break-even keys To reset the break-even keys to their default values, press ]OY. A brief message flashes on the screen to indicate the break-even registers have been reset. To return to the default calculator screen, press 112 Break-even M.
12 Statistical Calculations The 10bII+ allows you to enter data for one- and two-variable statistics easily. Once data is entered, you can use the statistical functions to calculate the following: • Mean and standard deviation • Regression statistics or a best fit • Estimation and forecasting • Weighted mean • Summation statistics: n, Σx, Σx2, Σ y, Σy2, and Σxy.
Clearing Statistical Data Clear the statistical data before entering new data. If you don't clear the statistical data, new information stored will be added to the current calculations. To clear all statistical data, press \t. The message STAT CLR flashes briefly and the display is cleared. The regression model is also reset to its default setting, LINEAR. Entering Statistical Data The 10bII+ uses a combination of list-based and register-based statistics when storing statistical data.
Figure 3 When the calculator switches to register-based mode, some key points to consider: • You may enter an unlimited number of data points. • The statistics editor, accessed with • While use of • The only regression mode available is a linear regression. v¡, is not available. \¢ is allowed, viewing previously entered data is not possible. One-Variable Statistics To enter x-data for one-variable statistics complete the following steps: 1. Clear the statistical registers by pressing 2.
Viewing and Editing Statistical Data 1. v¡ Press to open the editor. The number of items accumulated, n, is displayed, along with the current x-or y-value. The STAT annunciator appears, and the X or Y identifies the displayed value. 1 2. Press to move up through the current statistical data. When you pass the maximum of the data, an empty statistical pair displays before wrapping back to x1, provided there is enough memory for more data. 3. Press A to move down through the current statistical data.
At what temperature would the manager predict to sell 800 drinks? How many employees will be needed for tomorrow's predicted temperature of 43oC? Table 12-3 Example entering statistical data, opening the editor, and predicting Keys \t DGÆYJV¡ DVÆVJV¡ DgÆjGV¡ v¡ 11111 M ]LY Display STAT CLR Description Clears the statistics memory. (message flashes briefly, then disappears) 1.00 Enters first ordered pair. 2.00 Enters the second ordered pair. 3.00 Enters the third ordered pair. 1 32.
Table 12-4 Adding more data Keys YDÆJ:GD¡ DjÆSgV¡ Display Description 4.00 Enters fourth ordered pair. 5.00 Enters fifth ordered pair. After modifying the data, predict the next day’s activity at a record 45oC. Table 12-5 A new prediction Keys YV\W ]L: YV\W 118 Statistical Calculations Display Description 1,204.67 Predicts the drinks sold at 45oC. But is this the best fit? 0.00 Sets regression mode to 0-BEST FIT. 1,128.
Summary of Statistical Calculations The STAT annunciator indicates that a statistical calculation was performed. Some functions return two values. In this instance, the X annunciator is displayed along with STAT. Press \« to see the second value. In this case, the X annunciator changes to a Y, indicating the second value is being displayed. Table 12-6 Statistical calculations that return two values Keys Description \«Displays: \k \h Arithmetic mean (average) of the x-values.
Mean, Standard Deviations, and Summation Statistics You can calculate the mean ( x ), sample standard deviation (Sx), and population standard deviation ( σ x), and summation statistics, n, Σ x, and Σ x 2 of x-data. For x,y data, you can also calculate the mean, sample standard deviation, and population standard deviation of the ydata and the summation statistics Σ y, Σ y 2, and Σ xy. Example 2 A yacht captain wants to determine how long it takes to change a sail.
The standard deviations calculated by \h and \h\« are the sample standard deviations. They assume that the data is a sampling of a larger, complete set of data. If the data constitutes the entire population, the true population standard deviations can be calculated by pressing \e and \e\«. Example 3 The coach has four new players on the team with heights of 193, 182, 177, and 185 centimeters and weights of 90, 81, 83, and 77 kilograms.
Linear Regression. Calculate r (the correlation coefficient), m, b, and as follows: 1. Clear the statistical registers by pressing \t. Æ. The x-value is displayed. Enter the corresponding y-value and press ¡. The HP 10bII+ displays n, the number 2. Enter the first x-value and press 3. of pairs of items accumulated. 4. Continue entering x,y pairs. The n-value is increased with each entry. \Z\«. To display m, the slope, press \W\«. To display b (the y-intercept), press \T\«. 5.
Figure 4 Diagram on forecasting sales and minutes for advertising Table 12-10 Example for forecasting Keys \t GÆJY::¡ JÆdG:¡ DÆJJ::¡ VÆGGSV¡ VÆGgd:¡ YÆGG::¡ \T\« \W\« Display STAT CLR Description Clears statistics memory. (message flashes briefly, then disappears) 1.00 Enters minutes and sales for consecutive weeks. 2.00 3.00 4.00 5.00 6.00 376.25 Calculates y-intercept. 425.88 Displays slope.
Table 12-10 Example for forecasting Keys \Z\« Display 0.90 Description Calculates correlation coefficient. Estimate what the level of sales would be if the business purchased 7 or 8 minutes of advertising. Table 12-11 Estimating the level of sales Keys j\W g\W Display Description 3,357.38 Estimates sales if 7 minutes of advertising were purchased. 3,783.25 Estimates sales if 8 minutes were purchased.
Table 12-13 Calculating the average monthly rent Keys Display \t STAT CLR Description Clears statistics memory. (message flashes briefly, then disappears) V::ÆVY¡ V:VÆDG¡ VJ:Ægg¡ VJSÆdG¡ \T 1.00 Enters first rent and its weight. 2.00 Enters second rent and its weight. 3.00 Enters third rent and its weight. 4.00 Enters fourth rent and its weight. 509.44 Calculates the weighted mean.
If BEST FIT is selected, the 10bII+ calculates the best fit when \Z, \W, or \T is pressed. When selected, BEST FIT flashes briefly, followed by the chosen fit. The selected regression will remain set until a new one is selected, or the statistics memory is cleared. When the statistics memory is cleared using \t, the current regression model is set back to LINEAR.
Example Using five books labeled A, B, C, D, and E, how many different ways can three books be placed on a shelf? Table 12-15 Example calculating permutations Keys Display Description V]
Example Store a seed value of 42; set the number display to 9. Then generate three random numbers. Table 12-17 Example storing a seed value and generating random numbers Keys Display Description YG\w]6 \5d ]6 ]6 ]6 \5G 42.00 Stores 42 as the random number generator seed. 42.000000000 Set display precision. .199873749 Generate first random number. .863046890 Generate second random number. .504024868 Generate third random number. .50 Reset display to default setting.
Normal Lower Tail Probability To calculate the area under the curve to the left of z (the lower tail probability), enter the zvalue and press ]F . This function calculates the probability that a standard normal random variable, Z, is less than z. Figure 5 Example The variable Z is a standard normal random variable. What is the probability that Z is less than -1.7.? Table 12-19 Probability example Keys Display \5S J7jy]F Figure 6 Description .000000 Set display precision. .
Inverse of Normal Lower Tail Probability Figure 8 What is the z-value corresponding to a lower tail cumulative probability of .025? Table 12-20 Example calculating z-value (lower tail) Keys Display 7:GV]oF Figure 9 130 Statistical Calculations -1.959964 Description Calculate the corresponding zvalue.
Student's T Probability Lower Tail Figure 11 To calculate the area under the Student's T Distribution curve, first enter the degrees of freedom, followed by the t-value. It is a two-number function, so it may be entered as either an in-line function, or by using Æ. Example: What is the lower tail probability associated with a Student’s T distribution with 8 degrees of freedom (df1) with a t-value of -1.
Inverse of Student’s t Probability Lower Tail If you know the lower tail probability, P, and you want to calculate t, enter the degrees of freedom (df1), followed by Æ, then P. Press ]oIto calculate t. Figure 14 Example A hypothesis test requires a critical t-value from the Student’s T distribution with 26 degrees of freedom. Find the t-value for a lower tail probability of .05. Table 12-22 Example calculating the t-value (lower tail) Keys Display GS]oI7:V4 -1.
Conversions from Lower Tail The distribution functions on the 10bII+ return values for the lower tail cumulative probability. The lower tail probability corresponds to the area under the curve to the left of the given value. Sometimes you will want to work with areas other than the lower tail. It is easy to convert from lower tail to another area as long as you keep in mind that the total area under the curve is equal to 1, and the Normal and the Student’s T distributions are symmetrical.
Example 2 The variable Z is a standard normal random variable. What is the probability that z is greater than 1.2 or less than -1.2? Figure 18 The desired area is to the right of 1.2 and to the left of -1.2. Since normal distributions are symmetrical, and the areas are the same, you can calculate the lower tail area and simply multiply by 2. Table 12-24 Example converting from lower tail Keys Display Description J7Gy]F PG4 .115070 Calculate the lower tail area and store the value. .
Example 3 The variable Z is a standard normal random variable. Find z so that the probability that Z is less than z and greater than -z is equal to 0.95. Figure 19 The given area is 0.95. The area not included is 1-0.95/2 = 0.025. Since the normal distribution is symmetrical, half of the desired area is in the lower tail, .05/2=.025. The desired area corresponds to a lower tail probability of .025. Table 12-25 Example converting from lower tail (the inner area) Keys 7:GV]oF Display -1.
136 Statistical Calculations
13 Additional Examples Business Applications Setting a Sales Price One method for setting the per unit sales price is to determine the cost of production per unit, and then multiply by the desired rate of return. For this method to be accurate, you must identify all costs associated with the product. The following equation calculates unit price based on total cost and rate of return: PRICE = TOTAL COST ÷ NUMBER OF UNITS × (1 + (%RTN ÷ 100)) Example To produce 2,000 units, your cost is 40,000.
Table 13-3 Calculating the sales estimates for years six and seven Keys Display \t JÆJ::::¡ GÆJJGJ:¡ DÆJD:S:¡ YÆJS:jV¡ VÆG:Vd:¡ S\W j\W Description 0.00 Clears statistics registers. 1.00 Enters first year and sales for that year. 2.00 Enters second year’s data. 3.00 Continues data entry. 4.00 5.00 22,000.50 Estimates sales for year six. 24,605.00 Estimates sales for year seven.
Table 13-4 Calculating the cost without the cash discount Keys Display GPDS:PJ ::a \q\qJ: :AG\n P\qD:A J:4 72,000.00 Description Calculates numerator in equation. 98.00 Parentheses force order of calculation. 36.73 Calculates, as an annual percentage rate, cost of not taking discount. Loans and Mortgages Simple Annual Interest Example Your good friend needs a loan to start his latest enterprise and has asked you to lend him 450 for 60 days.
To solve a continuous compounding problem complete these steps: 1. Compute the annual effective rate using the above equation. 2. Either use this effective rate in your calculations with an annual period (P/YR = 1) or convert this rate so that it applies to your payment period. In the following example, P/YR = 12 so you have to calculate a new NOM% using the interest rate conversion application with P/YR equal to 12. Example You currently have 4,572.
Yield of a Discounted (or Premium) Mortgage The annual yield of a mortgage bought at a discount or premium can be calculated given the original mortgage amount (PV), interest rate (I/YR), periodic payment (PMT), balloon payment amount (FV), and the price paid for the mortgage (new PV). Remember the cash flow sign convention: money paid out is negative; money received is positive. Example An investor wishes to purchase a 100,000 mortgage taken out at 9% for 20 years.
Table 13-9 Calculating the balloon payment Keys Display Description V\Ú É 60.00 Stores number of payments until balloon. 88,706.74 Calculates the balloon payment (add to final payment). Step 3 Enter actual, current values for N and PV; then find the new I/YR for the discounted mortgage with balloon. Table 13-10 Keys Display Description vÙAYGÙ jd:::yÏ Ò 18.00 Stores remaining number of payments. -79,000.00 20.72 Stores price of mortgage. Calculates the return on this discounted mortgage.
Table 13-11 Calculating the annual percentage rate considering fees Keys Display Description D:\Ú JS::::Ï :É Ì vÏ -AG§Ï Ò 360.00 Stores length of mortgage. 160,000.00 Stores original amount of mortgage. 0.00 The loan will be completely paid off in 30 years. -1,230.26 Calculates payment. 160,000.00 Recalls loan amount. 156,800 8.72 Subtracts points. Calculates APR, considering fees.
Table 13-12 Calculating the annual percentage rate Keys Display Ò 12.53 Description Calculates APR. Loan With a Partial (Odd) First Period TVM calculations apply to financial transactions where each payment period is the same length. However, situations exist where the first payment period is not the same length as the remaining periods. This first period is sometimes called an odd or partial first period. If interest is applied to an odd first period, it is usually calculated as simple interest.
Table 13-13 Calculating the monthly payment amount Keys Display :É Ì 0.00 -157.03 Description Enters amount left to pay after 36 payments. Calculates the payment amount. Automobile Loan Example You are buying a new 14,000.00 sedan. Your down payment is 1,500 and you are going to finance the remaining 12,500. The car dealer is offering two choices for financing: • A 3-year loan with an annual interest rate of 3.5%. • A 3-year loan with an annual interest rate of 9.5% and a 1,000.00 rebate.
Table 13-15 Calculating the annual interest rate of 9.5% Keys d7VÒ Ì PvÙ4 Display Description 9.50 Stores second interest rate. -368.38 Calculates payment. -13,261.64 Calculates total interest and principal. The first option costs slightly less. Canadian Mortgages In Canadian mortgages, the compounding and payment periods are not the same. Interest is compounded semi-annually while payments are made monthly.
What if … TVM Calculations One of the most valuable aspects of the HP 10bII+’s TVM application is the ease with which it handles the question “what if …” in financial calculations. For example, one of the most popular “what if …” questions is, “What if the interest rate changes to …? How will that affect my payment?” To answer this question, once you have calculated a payment based on one interest rate, all you need to do is enter the new interest rate and recalculate PMT.
Table 13-18 Calculating the number of years required to pay off the loan Keys Display Description GS\Í Ù v\Ú 26.00 Sets payments per year for every two weeks. 514.82 Calculates number of biweekly payments. 19.80 Displays years required to pay off the loan.
Figure 20 Cash flow diagram Set to Begin mode. Press \¯ if BEGIN annunciator is not displayed. Table 13-20 Calculating the annual effective rate Keys Display d\Ó JG\Í \Ð Description 9.00 Stores annual nominal rate. 12.00 Stores number of compounding periods used with this nominal rate. 9.38 Calculates annual effective rate. When compounding occurs only once per year, the effective rate and the nominal rate are the same. Ò Set to Begin mode. Press 9.38 Stores effective rate as annual rate.
Then use that PV as the FV on the following cash flow diagram, and calculate the PMT. Figure 21 Cash flow diagram (Calculate PMT) Set to End mode. Press \¯ if BEGIN annunciator is displayed. Table 13-22 Calculating the monthly deposit required Keys yÉ :Ï JG\Í JYYÙ dÒ Ì Display 52,713.28 Description Stores amount you need. 0.00 Stores amount you are starting with. 12.00 Sets payments per year. 144.00 9.00 -204.54 Stores number of deposits. Stores interest rate.
account be? Assume that only the interest is taxed (assume the principal was taxed before deposit). What is the purchasing power of that amount, in today’s dollars, assuming a 4% inflation rate? Set to Begin mode. Press \¯ if BEGIN annunciator is not displayed. Table 13-23 Calculating the purchasing power of the amount Keys J\Í DVÙ g7JjVÒ :Ï G:::yÌ É vÌPvÙ4 1vÉ4 PJV§4 y1vÉ4 É YÒ:ÌÏ Display 1.00 35.00 Description Sets 1 payment per year. Stores number of periods and interest rate. 8.18 0.00 -2,000.
Example If you invest 3,000 each year for 35 years, with dividends taxed as ordinary income, how much will you have in the account at retirement? Assume an annual dividend rate of 8.175%, a tax rate of 28%, and that payments begin today. What is the purchasing power of that amount in today’s dollars, assuming 4% inflation? Set to Begin mode. Press \¯ if BEGIN annunciator is not displayed.
The payment calculation is a straightforward TVM payment calculation using the new amount as the PV. Set to End mode. Press \¯ if BEGIN annunciator is displayed. Table 13-25 Calculating the payment Keys Display ]OJ JG\Í gGVJ:7GG Ï d7VÒ :É JV\Ú Ì Description 0.00 Clears TVM registers. 12.00 Sets payments per year. 82,510.22 Stores loan amount on which your new payment is calculated. 9.50 Stores interest rate. 0.00 Stores final balance. 180.00 Stores number of monthly payments you will make.
N1 = 82 CF2 = 861.59 N2 = 180 - 82 = 98 Table 13-26 Calculating the annual return Keys Display DV:::y¤ vÌyAjVY ¤ gG\¥ vÌy¤ Jg:AgG\ ¥ \Á CF0 Description Enters 35,000 for loan amount. -35,000.00 CF1 107.59 n1 82.00 CF2 861.59 n2 Enters net payment for first 82 months. Enters number of times payment occurs. Enters net payment for next 98 months. 98.00 Enters number of times payment occurs. 10.16 Calculates annual return.
Appendix A: Batteries and Answers to Common Questions Power and Batteries The calculator is powered by two 3-volt lithium button-cell batteries, CR2032. When changing batteries, use only fresh button-cell batteries. Both batteries must be changed at the same time. Do not use rechargeable batteries. Low Power Annunciator When the low battery-power annunciator ( ) comes on, you should replace the batteries as soon as possible. If the battery annunciator is on and the display dims, you may lose data.
7. Insert the other new battery, making sure that the positive sign (+) battery is facing outward. 8. Replace the battery-compartment lid. 9. Press =. If the calculator does not turn on, follow the procedures below. Determining if the Calculator Requires Service Use these guidelines to determine if the calculator requires service. If these procedures confirm that the calculator is not functioning properly, refer to the Warranty, Environmental, and Contact Information located on the product CD.
The calculator responds to keystrokes, but you suspect that it is malfunctioning: 1. It is likely that you’ve made a mistake in operating the calculator. Try rereading portions of the manual, and check Answers to Common Questions below. 2. Contact the Calculator Support department. The contact information is listed on the product CD. Answers to Common Questions Hewlett-Packard is committed to providing you with ongoing support.
Q: How can I change the sign of a number in a list of cash flows? A: You must edit or replace the cash flow entry (Ch. 8 Cash Flow Calculations). Q: What does PEND in the display mean? A: An arithmetic operation is pending (in progress). Q: What does A:The INPUT in the display mean? Æ key has been pressed (Ch. 2 Getting Started). Q: Why is IRR/YR larger than I expected? A: This is IRR per year. To see a periodic IRR, divide IRR/YR by P/YR.
Appendix B: More About Calculations IRR/YR Calculations The calculator determines IRR/YR for a set of cash flows using mathematical formulas that search for the answer. The process finds a solution by estimating an answer and then using that estimate to do another calculation. This is called an iterative process. In most cases, the calculator finds the desired answer, since there is usually only one solution to the calculation. However, calculating IRR/YR for certain sets of cash flows is more complex.
Time Value of Money (TVM) Payment Mode Factor: S = 0 for End mode; 1 for Begin mode. I/YR i% = ------------P/YR –N i% ⎞ ⎞ ⎛ 1 – ⎛ 1 + -------⎝ ⎠ ⎟ ⎜ 100 i% × S 0 = PV + ⎛ 1 + ---------------⎞ × PMT × ⎜ --------------------------------------⎟ ⎝ i% 100 ⎠ ⎜ ⎟ -------⎝ ⎠ 100 i% + FV × ⎛ 1 + --------⎞ ⎝ 100⎠ –N Amortization ΣINT = accumulated interest ΣPRN = accumulated principal i = periodic interest rate BAL is initially PV rounded to the current display setting.
Cash-Flow Calculations i% = periodic interest rate. j = the group number of the cash flow. CFj = amount of the cash flow for group j. nj = number of times the cash flow occurs for group j. k = the group number of the last group of cash flows. Nj = ∑ n l = total number of cash flows prior to group j.
Bonds Reference: Lynch, John J. Jr. and Jan Mayle, Stanford Securities Calculation Methods, Securities Industry Association, New York, 1986. A = accrued days, the number of days from beginning of coupon period to settlement date. E = number of days in coupon bracketing settlement date. By convention, E is 180 (or 360) if calendar basis is 30/360. DSC = number of days from settlement date to next coupon date. (DSC= E - A). M = coupon periods per year (1 = annual, 2 = semiannual).
Depreciation For the given year number (YR) and with Factor (FACT) as a percentage: BASIS – SALV SL = ------------------------------------LIFE BASIS – SALV SOYD = ------------------------------------------------ × ( LIFE – YR + 1 ) ( LIFE + 1 ) LIFE × --------------------------2 FACT ⎛ FACT ---------------⎞ ⎞ BASIS × --------------- ⎛⎜ ⎝ 100 ⎠ ⎟ 100 DB = --------------------------------------- × ⎜ 1 – ---------------------⎟ LIFE LIFE ⎟ ⎜ ⎝ ⎠ ( YR – 1 ) For the last year of depreciation, DB equals the rema
Forecasting VI Name Fit Best Fit Automatically selects fit Linear m*x+b Logarithm m*ln(x)+b Exponential b*e(m*x) Power b*xm Exponent b*mx Inverse m/x+b Appendix B: More About Calculations
Appendix C: Messages Clear Messages Press M or | to clear a message from the display. Table C-1 Messages Message Displayed Description ALL CLEAR Memory has been erased (Ch. 2). COPR HP 2010 Copyright message. Oflo (Overflow). The magnitude of a result is too large for the calculator to handle. Message is displayed for a moment, then the overflow result is returned (±9.99999999999E499).
Table C-1 Messages Message Displayed Description BOND CLR bond registers were cleared. STAT CLR statistical memory and registers were cleared. Best Fit The calculator selected the best fit regression which is subsequently flashed for 1 second. running Displays if a calculation takes longer than .25 seconds. User Stop An IRR/YR, I/YR, or amortization calculation was interrupted by pressing II Appendix C: Messages M.
17 Warranty, Regulatory, and Contact Information Replacing the Batteries Warning! There is a danger of explosion if batteries are incorrectly replaced. Replace only with the same type of battery or with equivalent batteries (as recommended by the manufacturer). Dispose of used batteries according to the manufacturer’s instructions. Do not mutilate, puncture, or dispose of batteries in fire. The batteries can burst or explode, releasing hazardous chemicals.
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Perchlorate Material - special handling may apply This calculator's Memory Backup battery may contain perchlorate and may require special handling when recycled or disposed in California. Customer Care In addition to the one year hardware warranty, your HP calculator also comes with one year of technical support. If you need assistance with warranty, please refer to the warranty information on the product CD. HP customer care can be reached by either email or telephone.
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10 Warranty, Regulatory, and Contact Information
A Chain mode Advance payments 72 Algebraic mode calculations 28 Amortization 74 equations II range of payments 76 single payment 77 TVM keys used 75 Angle format selecting 35 Annuity account 70 Annunciators 30 Arithmetic operators 26 At a Glance Clearing quick reference guide 1 B Balloon payment 65 Batteries I installing I Battery replacing the batteries 1, 6 Bonds 105 clear memory 105 example 106 keys used 105 resetting bond keys 108 Break-even 109 example 16, 110 keys used 109 resetting keys 112
In-line functions 37 Interest mean of x weighted by y 113 means of x and y 113 MU (markup) 47 N 61 NFV 88 Nj 87 nom% 79 NPV 88 number of days 99 off 23 on 23 one-number functions 33 P/YR 61 parentheses 28 percent 45 period/comma 43 plus, minus, multiply, divide 26 PMT 61 population standard deviation 113 PRC (price business) 47 price (bonds) 105 profit (break-even) 109 PV 61 RAND 127 regression models 113 RND 43 sample standard deviation 113 semi/ann (bonds) 105 setdate (bonds) 105 shift keys 25 SL (straig
clearing II Messages I calculator status 44 list of I Registers M register 51 using numbered registers 51 Modes Regulatory Information 3 Reset II Rounding numbers 43 N S Negative numbers 29 Net future value 95 Net present value 95 Number of days 101 Number storage 49 Numbers display format 41 range of I Savings calculations 67 Scientific notation 43 Screen display iv Service II Statistics TVM begin and end 62 calculations that return two values 119 clearing data 114 entering data 114 keys used 1
